Chapter 12.4, Problem 43WE

To determine

Find the measure of angle $\left(\theta \right)$ to the nearest tenth of degree between $0°\text{ and }360°$ for the function $\cos \theta =0.4275$ and satisfy the condition $180°<\theta <360°$ .

Answer to Problem 43WE

The angle $\left(\theta \right)$ is equal to $295.3°$ .

Explanation of Solution

Given information: The given function is $\cos \theta =0.4275$ which satisfy the condition $180°<\theta <360°$ .

Calculation: The value of angle $\left(\theta \right)$ for the given function $\cos \theta =0.4275$ is evaluated as,

  $\begin{array}{c}\cos \theta =0.4275\\ \theta ={\cos }^{-1}\left(0.4275\right)\\ =64.7°\end{array}$

Now according to question $\cos \theta =0.4275$ is positive and the angle $\left(\theta \right)$ obtained is $64.7°$ which is also positive and lies in first quadrant but according to question $\left(\theta \right)$ must lie in third and fourth quadrant. Therefore angle $\left(\theta \right)$ which will lie in between third and fourth quadrant can be obtained by subtracting $64.7°$ from $360°$ .

  $\begin{array}{c}\theta =360°-64.7°\text{ for 0}°\text{<}\theta <180°\\ =295.3°\end{array}$